# Plotting ODE solutions with two parameters

I have a system of two first-order ODEs with two parameters, a and b and I'm trying to plot the solution curve in the X-Y plane at a given initial condition for various parameter values. Can someone give me a simple way of doing this? I've been experimenting with ParametricNDSolve but I'm new to Mathematica and I think I'm using it incorrectly. Any resources or information would be appreciated.

• use Manipulate, make sliders for the parameters, and do DSolve inside Manipulate and plot the solution(s). – Nasser Nov 24 '14 at 2:24
• There are examples in the documentation for ParametricNDSolve and ParametricNDSolveValue. If you showed how you're using it, someone might be able to point out any mistakes. – Michael E2 Nov 24 '14 at 3:10

eq = {  x'[t] Sin[y[ t]] + x[t] y'[t] a == 1, y'[t] Cos[x[t]] - y[t] x'[t] b == 1}
sol = ParametricNDSolve[{eq, x[0] == 1, y[0] == 1}, {x, y}, {t, 0,  1}, {a, b}]

Manipulate[ ParametricPlot[{x[a, b][t], y[a, b][t]} /. sol, {t, 0, 1},  AspectRatio -> 1],
{a, 0.5, 1}, {b, 0.5, 1}]